On 5 Jan, 02:39, David Bernier <david...@videotron.ca> wrote:> On 01/04/2013 12:07 PM, David Bernier wrote:> On 01/04/2013 10:46 AM, JT wrote:> >> On 4 Jan, 15:46, JT<jonas.thornv...@gmail.com> wrote:> >>> I remember doing this in a tentamen during my education in information> >>> theory beleiving what i did was binary sort but my teacher informed me> >>> it wasn't so what is it.>> [...]>>>>>>>>>> >> heap, what is the difference betwee a heap and a tree?).>> >> So what you think about the mix using this kind of sort for counting> >> in values, and then quicksort to sort the none null tree nodes by> >> sizes.>> > Oops.. below is about factoring. The best algorithms> > have been getting better since Maurice Kraitchik's [1920s]> > improvement on Fermat's method of expressing a number> > as a difference of squares, n = a^2 - b^2, so> > n = (a-b) (a+b).>> > There's a very good article called "A Tale of Two Sieves"> > by Carl Pomerance: Notices of the AMS, vol. 43, no. 12,> > December 1996:> > <http://www.ams.org/notices/199612/index.html>>> > The 9th Fermat number F_9 = 2^(512)+1 had been factored> > around 1990 by the Lenstras et al using the Number Field> > sieve (which had supplanted the quadratic sieve).>> > The Quadratic sieve is easier to understand than the> > Number Field Sieve, which I don't understand.>> > F_10 and F_11 were fully factored then, using the elliptic> > curve method (which can find smallish prime factors).>> > F_12 was listed as not completely factored, with> > F_12 being a product of 5 distinct odd primes and> > the 1187-digit composite:>> > C_1187 => > 22964766349327374158394934836882729742175302138572\>> [...]>> > 66912966168394403107609922082657201649660373439896\> > 3042158832323677881589363722322001921.>> > At 3942 bits for C_1187 above, what's the> > probability density function of expected time> > till C_1187 is fully factored?>> For the Fermat number F_12 = 2^(2^12) + 1 or> 2^4096 +1 , another prime factor was found around> 2010. So, this new prime factor would be a divisor> of C_1187, a 1187-digit number. F_12 is listed> as known to be "not completely factored".>> The relevant line on the Web-page referenced below contains> the text: "M. Vang, Zimmermann & Kruppa" in the "Discoverer"> column:> <http://www.prothsearch.net/fermat.html#Complete>>> Also, lower down in the page,> "50 digit k = 17353230210429594579133099699123162989482444520899">> This does relate to a factor of F_12 by PARI/gp.> Then, by my calcultions, the residual unfactored part> of F_12 has 1133 decimal digits and is a composite number.>> > Or, centiles: e.g. 50% chance fully factored> > within <= 10 years. 95% chance fully factored within> > <= 95 years, etc. ...>> Maybe 50% to 50% chances for "fully factored by 2100 " ?> (or 2060, or 2200 etc. ... )>> dave

I am not sure what you are implying here is sorting somehow related tofactorization, please explain in layman terms.